Final answer:
The total amount at the end of the 15th year of the series is approximately Rs. 231,703.72.
Step-by-step explanation:
To calculate the total amount at the end of the 15th year, we need to calculate the future value of the deposits made by the working woman. The deposits are increasing by Rs. 1,000 every year for 14 years. We can use the formula for future value of an annuity to calculate the total amount:
Future Value = P * ((1 + r)^n - 1) / r
Where P is the deposit amount, r is the interest rate per period, and n is the number of periods. In this case, the deposit amount is Rs. 5,000, the interest rate is 18% per year, and the number of periods is 14. Plugging in these values into the formula:
Future Value = 5000 * ((1 + 0.18)^14 - 1) / 0.18
Calculating this, we find that the future value of the deposits after 14 years is approximately Rs. 225,803.72. Now, we need to calculate the future value of the deposit made at the end of the first year. We can use the same formula with the deposit amount of Rs. 5,000, the interest rate of 18%, and the number of periods of 1:
Future Value = 5000 * ((1 + 0.18)^1 - 1) / 0.18
Calculating this, we find that the future value of the deposit after 1 year is approximately Rs. 5,900. Adding these two future values, we can calculate the total amount at the end of the 15th year:
Total Amount = Rs. 225,803.72 + Rs. 5,900 = Rs. 231,703.72
Therefore, the total amount at the end of the 15th year of the series is approximately Rs. 231,703.72.